Brodziak, 35, has not played this season and is on long-term injured reserve because of a back injury. He is in the final season of a two-year, $2.3 million contract, with an annual cap hit of $1.15 million.
The draft pick will either be a fourth-round selection in the 2020 NHL Entry Draft or a third-round selection in the 2021 draft if the Oilers reach the final four and Green plays in 50 percent of the games.
According to TSN and The Athletic's Pierre LeBrun, the Wings will also retain 50 percent of Green's salary and cap hit.
LeBrun also said that Green agreed to waive his modified no-trade clause.
After this past Saturday's practice at the BELFOR Training Center, Green said he had gotten accustomed to hearing his name in trade rumors and tried to focus on things he could control.
But Green admitted there would be mixed emotions if a contending team wanted to trade for him.
"Until it happens, you don't feel the emotions," Green said Saturday. "Obviously when you bring it up, inside of you, you have a tie. There's a lot of memories. But nothing's happened, so I'm not overthinking things. I'm just making sure I do my job day to day, like I said. Anytime you leave a job, any sort of team, it doesn't matter what it is. There's emotions involved."
Monday afternoon, Green thanked Detroit fans on social media.